The Definition of the Grading Scales in Banks’ Internal Rating Systems

Abstract

A. FOGLIA^S. IANNOTTI^P. MARULLO REEDTZ Ã An internal risk rating system can be de®ned as the process used to classify bank borrowers into categories of different credit riskiness. Most of the related literature has investigated various aspects of this process, but the problem of de®ning the categories and the distribution of borrowers into the different classes or grades has received rather less attention, other than noting that the number of grades and their dispersion should achieve a meaningful differentiation of risk. An appropriate de®nition of the grading scale is of primary importance because the probability of default associated to each grade is the key inputs of capital allocation systems at many best-practice banks and is the core of the January 2001's new proposal of the Basel Committee for the calculation of capital requirements. Statistical techniques such as cluster analysis can help in identifying distinct subgroups of borrowers possessing the same creditworthiness. We use a logit model to estimate individual default probabilities for four categories of borrowers and apply cluster analysis to assign borrowers to each grade. However, since cluster analysis is not a purely mechanical process, but requires examination of the nature of observations and of the objective of clustering, the ultimate choice of the most appropriate grading scale for a given portfolio relies on empirical grounds. A suf®cient granularity and an appropriate quanti®cation of risk must be balanced.(

The optimal structure of PD buckets

“…This suggests that a careful selection of the best bucket structure, as opposed to naïve approaches that do not take the bank's actual customer base into account, can indeed be advantageous (in terms Foglia et al (2001) would produce a 0.34 bps mean error (euroweighted) and allocate more than 80% of the clients to the first bucket. 24 Indeed, rather than charging high-risk obligors with extremely high spreads, banks tend to ration credit to them in order to avoid adverse selection issues (Stiglitz and Weiss, 1981) and defaults triggered by high interest expenses.…”

“…Here the main idea is to view the PD bucketing problem as a clustering problem, where one has to find the optimal partition of all obligors, such that the sum of the errors within the groups (here: risk buckets) is minimized. Following this approach, Foglia et al (2001), used k-means clustering to determine the partition into 7, 10 and 15 buckets of a large sample of Italian firms period in 1995-1998. The k-means algorithm is one of the most popular non-hierarchical clustering algorithms, because it is easy to implement and fast, due to its linear runtime complexity.…”

“…Furthermore, the standard k-means algorithm cannot deal with constraints related to the clusters composition. To our knowledge, the k-means approach used by Foglia et al (2001) is the only published contribution about using error-based statistics for PD bucketing in an empirical study. (2004), § § 403-406.…”

“…One approach consists of an extension of the error-based approach proposed by Foglia et al (2001) that introduces realistic constraints on buckets. The other approach aims at minimizing loan-pricing errors and hence the adverse selection phenomena mentioned in Section 1.…”

“…While the objective function in (1) is similar to the one underlying the k-means algorithm implemented by Foglia et al (2001), our approach is more general and can easily accommodate constraints on the bucket structure (e.g. minimum and maximum limits on the number of customers associated with individual buckets), as well as changes in the objective functions aimed at making it more realistic.…”